1. In Lecture 10 we derived optimal acquisition and sorting policies in the case of used product condition variability. Assume that used products are acquired for a unit cost of $2. Condition is exponentially distributed with rate = 0.2, implying an average cost to remanufacture of $5. Unit sales revenue is $10 and unit shortage penalty is $3. Demand has a continuous uniform distribution between 500 and 1500.

   (a) Find the optimal fraction of acquired used products that must be remanufactured. (b) Find the optimal number of used products that must be remanufactured. (c) Find the optimal number of used products that must be acquired.